Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
113 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 113 conjugacy classes of subgroups — too many to draw. Only its 26 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 576 |
Polycyclic presentation:
2^3,3^2,2^3|a^2=h,b^2=c,d^3=e^2,f^2=h,g^2=h,b^a=bh,d^a=d^2e,e^a=e^2,f^a=gh,g^a=fh,f^d=g,g^d=fgh,g^f=gh54 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10589490, #11920218, C4×#63689, … |
| maximal normal subgroup of | C2×#10589490, #11920218, C4×#63689, … |
| maximal quotient of | #3688⋊C8, #11919964, #11920014, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1372);